Szczegóły publikacji
Opis bibliograficzny
Efficient finite-dimensional solution of initial value problems in infinite-dimensional Banach spaces / Bolesław KACEWICZ, Paweł PRZYBYŁOWICZ // Journal of Mathematical Analysis and Applications ; ISSN 0022-247X. — 2019 — vol. 471 iss. 1–2, s. 322–341. — Bibliogr. s. 340–341, Abstr. — Publikacja dostępna online od: 2018-10-30
Autorzy (2)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 118363 |
|---|---|
| Data dodania do BaDAP | 2018-12-05 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jmaa.2018.10.077 |
| Rok publikacji | 2019 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Mathematical Analysis and Applications |
Abstract
We deal with the approximate solution of initial value problems in infinite-dimensional Banach spaces with a Schauder basis. We only allow finite-dimensional algorithms acting in the spaces RN, with varying N. The error of such algorithms depends on two parameters: the truncation parameters Nand a discretization parameter n. For a class of Crright-hand side functions, we define an algorithm with varying N, based on possibly non-uniform mesh, and we analyzeits error and cost. For constant N, we show a matching (up to a constant) lower bound on the error of any algorithm in terms of Nand n, as N, n →∞. We stress that in the standard error analysis the dimension Nis fixed, and the dependence on Nis usually hidden in error coefficient. For a certain model of cost, for many cases of interest, we show tight (up to a constant) upper and lower bounds on the minimal cost of computing an ε-approximation to the solution (the ε-complexity of the problem). The results are illustrated by an example of the initial value problem in the weighted lp space (1 ≤p <∞).